Localization criteria for Anderson models on locally finite graphs

TL;DR

This paper proves spectral and dynamical localization for Anderson models on locally finite graphs, extending previous results on ^d, using the fractional moment method under certain geometric conditions.

Contribution

It introduces geometric assumptions on graphs that ensure localization for the Anderson model at high disorder levels, broadening the class of graphs where localization is established.

Findings

Localization proven for a broad class of graphs

Spectral and dynamical localization established

Results extend previous ^d localization findings

Abstract

We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on $\ZZ^d$. We establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently large disorder.